Different types of spdes in the eyes of girsanov's theorem
Different types of spdes in the eyes of girsanov's theorem
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吉尔萨诺夫定理眼中不同类型的spdes
DOI：
10.1080/07362999808809562
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发表时间：
1998
影响因子：
1.3
通讯作者：
Hassan Allouba
中科院分区：
文献类型：
--
作者：
Hassan Allouba
证明了连续正交鞅测度的Girsanov定理。然后，我们定义空间-时间的SDES，并使用Girsanov定理建立一个一对一的对应关系的解决方案的两个空间-时间的SDES不同，只有一个漂移系数。对于这类随机方程，我们给出了它们的解的律彼此绝对连续的必要条件。再次利用Girsanov定理，我们证明了时空偏微分方程的存在唯一性结果。对于随机热方程和波动方程也证明了同样的一一对应和绝对连续性定理
We prove Girsanov's theorem for continuous orthogonal martingale measures. We then define space-time SDEs, and use Girsanov's theorem to establish a oneto- one correspondence between solutions of two space-time SDEs differing only by a drift coefficient. For such stochastic equations, we give necessary conditions under which the laws of their solutions are absolutely continuous with respect to each other. Using Girsanov's theorem again, we prove additional existence and uniqueness results for space-time SDEs. The same one-to-one correspondence and absolute continuity theorems are also proved for the stochastic heat and wave equations